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Finding the Fourth Proportional to 1,584, 2,376 and 429.75

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Solution

The fourth proportional to 1,584, 2,376 and 429.75 is: 644.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,584 : 2,376 = 429.75 : x
  2. Step 2: Convert to fraction form
    1,584/2,376 = 429.75/x
  3. Step 3: Cross multiply
    1,584x = 2,376 × 429.75
  4. Step 4: Simplify right side
    1,584x = 1,021,086
  5. Step 5: Solve for x
    x = 1,021,086/1,584
  6. Step 6: Final answer
    x = 644.63

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.